The arm for a quadratic off the real line excludes the arms on the sign of its discriminant

[Rafael-SOWNet]

Part of #1788.

An antiderivative over a quadratic with i among its coefficients has an arm off the real line, not D in RR or D > 0, beside the arms D = 0 and D < 0. A sum of two such answers pairs their arms and drops a pair whose conditions contradict each other, and that arm was read against neither -- though D = 0 asks D to be real, and D < 0 is NaN off the real line, so neither pairing is ever true:

integrand	2.5.0	master 15aae3d3	this
x^2/(x^2 + a + i b)^3	10 arms, no value at a real x	7 arms, 2,701 characters	3 arms, 1,065 characters
1/(x^2 + i a)^2 + 1/(x^2 + i a)^3	9 arms, no value at a real x	7 arms, 1,994 characters	3 arms, 779 characters

What changes. The test CombinedCaseByCase puts each pair through reads its conjuncts as tests of a quantity against zero. It reads not q in RR as one now, which an equality contradicts for every value and a strict sign for a real q, NaN off the real line being no truer; and a disjunction as contradicted where each of its arms is, for every value or for the same quantity. A pair that is contradicted for a real q only goes where every later pair tests the sign of q, as before.

This is the third of three defects in the size of #1788's answers; with all three, 2 d^3 t^2/((t^2 - c - i d)^3 (t^2 - c + i d)) has 9 arms where master writes 63.

Tests: ContradictoryConjunctionTest.TheArmOffTheRealLineExcludesTheSignArms: the sum of two piecewises with that arm and the two signs has three cases, and a chain of four more stays at three, with values on each side of zero, at zero and off the real line. It fails on master's code.

Measured on every corpus problem with i in its integrand, 2,253 of them, at the corpus's 5-second budget, against master 221d3c5f, the branch's base:

	master	this
solved	1838	1838
unevaluated	140	140
wrong	1	1
past the budget	210	211

One answer is counted wrong on each build, and the two builds answer and decline the same problems.

The one problem the two builds disagreed on, run again one build at a time, gets the same verdict from both. Nothing is answered or declined differently; the answers are shorter.

The suite on the commit measured, 6688a0e3, passes, 15,036 tests, and so does the allocation gate: every gated benchmark allocates what the baseline says. The head here, 6da62f53, merges master 15aae3d3; the calculus and corpus tests pass on it, 4,358 tests, and the library builds for netstandard2.0.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura